Related papers: Hill's Equation with Random Forcing Terms
We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the…
We study a spatially explicit harvesting model in periodic or bounded environments. The model is governed by a parabolic equation with a spatially dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative external…
We study the second order elliptic equations of non-divergence form in a planar domain with complicated geometry. In this case the domain winds around a fixed circle infinitely many times and converges to it when the rotating angle goes to…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
A dynamic mitigation mechanism for instability growth was proposed and discussed in the paper [Phys. Plasmas 19, 024503 (2012)]. In the present paper the robustness of the dynamic instability mitigation mechanism is discussed further. The…
The Cahn-Hilliard and viscous Cahn-Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved. Key words: Cahn-Hilliard…
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
Random dynamical systems (RDS) evolve by a dynamical rule chosen independently with a certain probability, from a given set of deterministic rules. These dynamical systems in an interval reach a steady state with a unique well-defined…
In this paper we will deduce several properties of the Green's functions related to the Hill's equation coupled to various boundary value conditions. In particular, the idea is to study the Green's functions of the second order differential…
The aim of this paper is to give a result concerning the stability properties of the solutions of magnetohydrodynamics equations at small but finite Reynolds numbers. These solutions are found using the alpha-effect: this method gives us…
Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…
We study the work distribution of a single particle moving in a harmonic oscillator with time-dependent strength. This simple system has a non-Gaussian work distribution with exponential tails. The time evolution of the corresponding moment…
This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from…
A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a…
We develop a formulation of the strong deflection limit for the scattering of particles following timelike geodesics in asymptotically flat, static, and spherically symmetric spacetimes. For fixed specific energy, as the angular momentum…
In this paper, we provide a result of exponential stability for several dissipative linear kinetic equations with heavy-tailed equilibria. The approach, inspired by the so-called $L^2$-hypocoercivity method, is robust enough to provide…
The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a…
The turbulent dynamo effect, which describes the generation of magnetic fields in astrophysical objects, is described by the dynamo equation. This, in the kinematic (linear) approximation gives an unbounded exponential growth of the long…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers…